I took a quick look thru the Sony W690 user manual, and it looks like there's no option for freely chosen text (your name) being added on the photos.

But you can do it with a photo editor, only it happens in computer, not in-camera. The word "watermark" sounds a bit too fancy, when at its simplest form it could be just plain text drawn over the photo, preferably in a corner or such a spot where it does not jump on your face when looking at the photo. See "How do I position a watermark?"

You can also add your name and other info inside the photo so that it does not become visible on the photo but stays inside the data of the file. That info is called metadata, and also with word EXIF. You can use a photoeditor to write into metadata, or with some cameras you can put some info automatically into each and every photo you take. See "Adding data to an EXIF file". Though that info stays inside the file and is not showing on the photo if and when you print it on paper.